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// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.
//
// Copyright (c) DUSK NETWORK. All rights reserved.
use core::cmp::{Ord, Ordering, PartialOrd};
use core::convert::TryInto;
use core::ops::{Index, IndexMut};
use dusk_bls12_381::BlsScalar;
use dusk_bytes::{Error as BytesError, Serializable};
use super::{Fr, MODULUS, R2};
use crate::util::sbb;
#[cfg(feature = "zeroize")]
impl zeroize::DefaultIsZeroes for Fr {}
impl Fr {
/// Creates a `Fr` from arbitrary bytes by hashing the input with BLAKE2b
/// into a 512-bits number, and then converting the number into its scalar
/// representation by reducing it by the modulo.
///
/// By treating the output of the BLAKE2b hash as a random oracle, this
/// implementation follows the first conversion of
/// https://hackmd.io/zV6qe1_oSU-kYU6Tt7pO7Q with concrete numbers:
/// ```text
/// p = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
/// p = 6554484396890773809930967563523245729705921265872317281365359162392183254199
///
/// l = 2
///
/// s^l = (2^256)^2 = 2^512
/// s = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
///
/// r' = 2045593080716281616348203381729468609728209645786990242449482205581148743408809
///
/// m' = 2244478849891746936202736009816130624903096691796347063256129649283183245105
/// ```
pub fn hash_to_scalar(input: &[u8]) -> Self {
let state = blake2b_simd::Params::new()
.hash_length(64)
.to_state()
.update(input)
.finalize();
let bytes = state.as_bytes();
Self::from_u512([
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[0..8]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[8..16]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[16..24]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[24..32]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[32..40]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[40..48]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[48..56]).unwrap()),
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[56..64]).unwrap()),
])
}
/// SHR impl: shifts bits n times, equivalent to division by 2^n.
#[inline]
pub fn divn(&mut self, mut n: u32) {
if n >= 256 {
*self = Self::from(0u64);
return;
}
while n >= 64 {
let mut t = 0;
for i in self.0.iter_mut().rev() {
core::mem::swap(&mut t, i);
}
n -= 64;
}
if n > 0 {
let mut t = 0;
for i in self.0.iter_mut().rev() {
let t2 = *i << (64 - n);
*i >>= n;
*i |= t;
t = t2;
}
}
}
/// Reduces bit representation of numbers, such that
/// they can be evaluated in terms of the least significant bit.
pub fn reduce(&self) -> Self {
Fr::montgomery_reduce(
self.0[0], self.0[1], self.0[2], self.0[3], 0u64, 0u64, 0u64, 0u64,
)
}
/// Evaluate if a `Scalar, from Fr` is even or not.
pub fn is_even(&self) -> bool {
self.0[0] % 2 == 0
}
/// Compute the result from `Scalar (mod 2^k)`.
///
/// # Panics
///
/// If the given k is > 32 (5 bits) as the value gets
/// greater than the limb.
pub fn mod_2_pow_k(&self, k: u8) -> u8 {
(self.0[0] & ((1 << k) - 1)) as u8
}
/// Compute the result from `Scalar (mods k)`.
///
/// # Panics
///
/// If the given `k > 32 (5 bits)` || `k == 0` as the value gets
/// greater than the limb.
pub fn mods_2_pow_k(&self, w: u8) -> i8 {
assert!(w < 32u8);
let modulus = self.mod_2_pow_k(w) as i8;
let two_pow_w_minus_one = 1i8 << (w - 1);
match modulus >= two_pow_w_minus_one {
false => modulus,
true => modulus - ((1u8 << w) as i8),
}
}
/// Computes the windowed-non-adjacent form for a given an element in
/// the JubJub Scalar field.
///
/// The wnaf of a scalar is its breakdown:
/// scalar = sum_i{wnaf[i]*2^i}
/// where for all i:
/// -2^{w-1} < wnaf[i] < 2^{w-1}
/// and
/// wnaf[i] * wnaf[i+1] = 0
pub fn compute_windowed_naf(&self, width: u8) -> [i8; 256] {
let mut k = self.reduce();
let mut i = 0;
let one = Fr::one().reduce();
let mut res = [0i8; 256];
while k >= one {
if !k.is_even() {
let ki = k.mods_2_pow_k(width);
res[i] = ki;
k -= Fr::from(ki);
} else {
res[i] = 0i8;
};
k.divn(1u32);
i += 1;
}
res
}
}
// TODO implement From<T> for any integer type smaller than 128-bit
impl From<i8> for Fr {
// FIXME this could really be better if we removed the match
fn from(val: i8) -> Fr {
match (val >= 0, val < 0) {
(true, false) => Fr([val.unsigned_abs() as u64, 0u64, 0u64, 0u64]),
(false, true) => -Fr([val.unsigned_abs() as u64, 0u64, 0u64, 0u64]),
(_, _) => unreachable!(),
}
}
}
impl From<Fr> for BlsScalar {
fn from(scalar: Fr) -> BlsScalar {
let bls_scalar =
<BlsScalar as Serializable<32>>::from_bytes(&scalar.to_bytes());
// The order of a JubJub's Scalar field is shorter than a BLS
// Scalar, so convert any jubjub scalar to a BLS' Scalar
// should always be safe.
assert!(
bls_scalar.is_ok(),
"Failed to convert a Scalar from JubJub to BLS"
);
bls_scalar.unwrap()
}
}
impl Index<usize> for Fr {
type Output = u64;
fn index(&self, _index: usize) -> &u64 {
&(self.0[_index])
}
}
impl IndexMut<usize> for Fr {
fn index_mut(&mut self, _index: usize) -> &mut u64 {
&mut (self.0[_index])
}
}
impl PartialOrd for Fr {
fn partial_cmp(&self, other: &Fr) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for Fr {
fn cmp(&self, other: &Self) -> Ordering {
let a = self;
for i in (0..4).rev() {
#[allow(clippy::comparison_chain)]
if a[i] > other[i] {
return Ordering::Greater;
} else if a[i] < other[i] {
return Ordering::Less;
}
}
Ordering::Equal
}
}
impl Serializable<32> for Fr {
type Error = BytesError;
/// Attempts to convert a little-endian byte representation of
/// a field element into an element of `Fr`, failing if the input
/// is not canonical (is not smaller than r).
fn from_bytes(bytes: &[u8; Self::SIZE]) -> Result<Self, Self::Error> {
let mut tmp = Fr([0, 0, 0, 0]);
tmp.0[0] = u64::from_le_bytes(bytes[0..8].try_into().unwrap());
tmp.0[1] = u64::from_le_bytes(bytes[8..16].try_into().unwrap());
tmp.0[2] = u64::from_le_bytes(bytes[16..24].try_into().unwrap());
tmp.0[3] = u64::from_le_bytes(bytes[24..32].try_into().unwrap());
// Try to subtract the modulus
let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
// If the element is smaller than MODULUS then the
// subtraction will underflow, producing a borrow value
// of 0xffff...ffff. Otherwise, it'll be zero.
let is_some = (borrow as u8) & 1;
if is_some == 0 {
return Err(BytesError::InvalidData);
}
// Convert to Montgomery form by computing
// (a.R^0 * R^2) / R = a.R
tmp *= &R2;
Ok(tmp)
}
/// Converts an element of `Fr` into a byte representation in
/// little-endian byte order.
fn to_bytes(&self) -> [u8; Self::SIZE] {
// Turn into canonical form by computing
// (a.R) / R = a
let tmp = Fr::montgomery_reduce(
self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0,
);
let mut res = [0; Self::SIZE];
res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
res
}
}
#[test]
fn w_naf_3() {
let scalar = Fr::from(1122334455u64);
let w = 3;
// -1 - 1*2^3 - 1*2^8 - 1*2^11 + 3*2^15 + 1*2^18 - 1*2^21 + 3*2^24 +
// 1*2^30
let expected_result = [
-1i8, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 3, 0, 0, 1, 0, 0,
-1, 0, 0, 3, 0, 0, 0, 0, 0, 1,
];
let mut expected = [0i8; 256];
expected[..expected_result.len()].copy_from_slice(&expected_result);
let computed = scalar.compute_windowed_naf(w);
assert_eq!(expected, computed);
}
#[test]
fn w_naf_4() {
let scalar = Fr::from(58235u64);
let w = 4;
// -5 + 7*2^7 + 7*2^13
let expected_result = [-5, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7];
let mut expected = [0i8; 256];
expected[..expected_result.len()].copy_from_slice(&expected_result);
let computed = scalar.compute_windowed_naf(w);
assert_eq!(expected, computed);
}
#[test]
fn w_naf_2() {
let scalar = -Fr::one();
let w = 2;
let two = Fr::from(2u64);
let wnaf = scalar.compute_windowed_naf(w);
let recomputed = wnaf.iter().enumerate().fold(Fr::zero(), |acc, (i, x)| {
if *x > 0 {
acc + Fr::from(*x as u64) * two.pow(&[(i as u64), 0u64, 0u64, 0u64])
} else if *x < 0 {
acc - Fr::from(-(*x) as u64)
* two.pow(&[(i as u64), 0u64, 0u64, 0u64])
} else {
acc
}
});
assert_eq!(scalar, recomputed);
}
#[cfg(all(test, feature = "alloc"))]
mod fuzz {
use alloc::vec::Vec;
use crate::fr::{Fr, MODULUS};
use crate::util::sbb;
fn is_scalar_in_range(scalar: &Fr) -> bool {
// subtraction against modulus must underflow
let borrow = scalar
.0
.iter()
.zip(MODULUS.0.iter())
.fold(0, |borrow, (&s, &m)| sbb(s, m, borrow).1);
borrow == u64::MAX
}
quickcheck::quickcheck! {
fn prop_hash_to_scalar(bytes: Vec<u8>) -> bool {
let scalar = Fr::hash_to_scalar(&bytes);
is_scalar_in_range(&scalar)
}
}
}
#[cfg(feature = "zeroize")]
#[test]
fn test_zeroize() {
use zeroize::Zeroize;
let mut scalar = Fr::one();
scalar.zeroize();
assert_eq!(scalar, Fr::zero());
}